Decomposition of Space-Variant Blur in Image Deconvolution

Standard convolution as a model of radiometric degradation is in majority of cases inaccurate as the blur varies in space and we are thus required to work with a computationally demanding space-variant model. Space-variant degradation can be approximately decomposed to a combination of standard convolutions and point-wise multiplications. The space-variant degradation operator contains different filters in columns and rows as illustrated in the following figure:

Decomposition can be carried out row-wise or column-wise. We propose a computationally efficient space-variant deconvolution algorithm that belongs to a category of alternating direction methods of multipliers, which consists of four update steps with closed-form solutions. Depending on the used decomposition, two variations of the algorithm exist with distinct properties. You can download the code here.

Examples on real data:

Video frame from a traffic camera (Courtesy of Lukáš Maršík from CAMEA)

cropped region used for deconvolution

space-invariant deconvolution

space-variant deconvolution

JPEG image captured with a DSLR camera. A raw image was captured simultanously and used for reconstruction.